The use of large-deflection tire models to predict vehicle loads for design or simulation testing has become an important application in the automotive vehicle development process. A wide range of tire models have been used to simulate the tire. In general, current tire models can be divided into three categories: simple models, ring elastic foundation (REF) models, and detailed models.
Two simple tire models are shown in FIGS. 1 and 2. These models assume that the tire envelopes an obstacle and that the effect the tire tread has on contact and deformation is negligible. In a radial spring model (FIG. 1), the tire envelopes the terrain with springs that are radially attached to center of the tire. Another simple model, commonly referred to as an ADAMS model (FIG. 3), uses an "equivalent ground plane" to calculate the longitudinal and vertical spindle forces. In both models, the net spindle force is generated by summing the individual spring forces in the vertical and horizontal directions.
In contrast to simple models, a Ring Elastic Foundation (REF) model represents the tire as an elastic foundation supporting a tread. REF models can be represented either with partial differential equations or with finite elements. Detailed tire models are three dimensional finite element representations of the complete tire (FIG. 4). These models are more representative of an actual tire than the previously discussed models, but a major disadvantage of this type of model is the large number of degrees-of-freedom needed and consequently the intensive computing time required.
Many existing tire models use a finite element analysis (FEA) approach to determine vehicle loads. However, these currently available models have inaccurately estimated tire loads through computer simulation. In addition, all of the tire finite-element models discussed above are time-intensive to build and run. Vehicle spindle-coupled simulation requires a tire model that is relatively easy to model from readily-measurable parameters, which is not computationally intensive, and which is easy to implement with a spindle-coupled simulation controller utilizing an effective road profile.
A tire model to meet the just described requirements was disclosed in U.S. patent application Ser. No. 08/585,675, now U.S. Pat. No. 5,750,890, assigned to the assignee of the present invention and incorporated herein by reference. In that application, a method and apparatus for acquiring input and output data was disclosed, as was a coordinate system for defining an effective road profile. The coordinate system, defined three-dimensionally, was selected to represent a `flat surface road plane` with a plane vertical deflection at the tire patch center, a plane radial contact angle with the tire, and a plane lateral contact angle with the tire. However, a more accurate tire model is desirable to further identify tire dynamics.